let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

We define a theta operator between spaces of Siegel modular forms (mod p), generalizing the theta operator for (elliptic) modular forms.

We show that there is an operator space notion of Lipschitz embeddability between spaces which strictly weaker than its linear counterpart but still strong enough to impose restrictions on structures. This shows a nontrivial theory nonlinear geometry for and it answers question in Braga et al. (Proc Am Math Soc 149(3):1139–1149, 2021). For that, we introduce the version Lipschitz-free Banach pr...

Let A be a sectorial operator on a non-atomic Lp-space, 1 ≤ p < ∞, whose resolvent consists of integral operators, or more generally, has a diffuse representation. Then the fractional domain spaces D(Aα) for α ∈ (0, 1) do not coincide with the real interpolation spaces of (Lq , D(A)). As a consequence, we obtain that no such operator A has a bounded H∞-calculus if p = 1.

*Correspondence: [email protected] Department of Mathematics, Tianjin University of Technology, Tianjin, 300000, P.R. China Abstract The aim of this paper is to introduce the normed binomial sequence spaces br,s p (∇) by combining the binomial transformation and difference operator, where 1≤ p≤∞. We prove that these spaces are linearly isomorphic to the spaces p and ∞, respectively. Furtherm...

Let T be the Calderón-Zygmund singular integral operator, a well-known result of Coifman et al. (see [6]) states that the commutator [b,T]( f ) = T(b f )− bT( f ) (where b ∈ BMO) is bounded on Lp(Rn) (1 < p <∞); Chanillo (see [1]) proves a similar result when T is replaced by the fractional integral operator; in [8, 9], these results on the TriebelLizorkin spaces and the case b ∈ Lipβ (where Li...

Let T be the singular integral operator, a well-known result of Coifman, Rochberg and Weiss [6] which states that the commutator [b,T ] = T (b f )− bT f (where b ∈ BMO) is bounded on Lp(Rn)(1 < p < ∞). Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. In [9,11], these results on the Triebel–Lizorkin spaces and the case b∈Lipβ (where Lipβ is the homogen...

In this paper, we prove the Spanne-Guliyev type boundedness of the generalized fractional integral operator Iρ from the vanishing generalized local Morrey spaces V LM {x0} p,φ1 to V LM {x0} q,φ2 , 1 < p < q < ∞, and from the space V LM {x0} 1,φ1 to the weak space VWLM {x0} q,φ2 , 1 < q < ∞. We also prove the Adams-Guliyev type boundedness of the operator Iρ from the vanishing generalized Morrey...